After going over all the "ports and pins" and plug in configurations several times I found the answer to my own question. I couldn't understand how an axis could move with the Mach3 jog control and not with a Mach3 program run. But things are complex and I sure don't understand everything by a long shot. By comparing the complicated and somewhat mysterious settings in the plugin configuration screens (there is a whole page for each axis as well as a page of system settings) for the X and Y to the Z, I found a difference and changed it to be like the X and Y. Now everything is working normally. Most likely I accidentally clicked on the setting while following the setup instructions, but could also be an error in the XML document used configure the plugin. Now all three axis work fine. Just to be sure I machined a small helix and it came out perfect.